共查询到20条相似文献,搜索用时 93 毫秒
1.
Amol Sasane 《Complex Analysis and Operator Theory》2009,3(1):323-330
Let E be a separable infinite-dimensional Hilbert space, and let denote the algebra of all functions that are holomorphic. If is a subalgebra of , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra , the disk algebra and the Wiener algebra are all infinite.
Submitted: October 10, 2007., Revised: January 11, 2008., Accepted: January 12, 2007. 相似文献
2.
Hari Bercovici 《Complex Analysis and Operator Theory》2007,1(3):335-339
Consider a domain
, and two analytic matrix-valued functions functions
. Consider also points
and positive integers n
1, n
2, . . . , n
N
. We are interested in the existence of an analytic function
such that X(ω) is invertible, and G(ω) coincides with X(ω)F(ω)X(ω)−1 up to order n
j
at the point ω
j
. We will see that such a function exists provided that F(ω
j
),G(ω
j
) have cyclic vectors, and the characteristic polynomials of F,G coincide up to order n
j
at ω
j
. This allows one to give a short proof to a result of Huang, Marcantognini and Young concerning spectral interpolation in
the unit disk.
The author was partially supported by a grant from the National Science Foundation.
Received: September 8, 2006. Accepted: January 11, 2007. 相似文献
3.
Amol Sasane 《Integral Equations and Operator Theory》2007,59(2):245-256
Let E, E* be separable Hilbert spaces. If S is an open subset of
, then
denotes the space of all functions
that are holomorphic in
, and bounded and continuous on
. In this article we prove the following results:
相似文献
1. | A theorem concerning the approximation of by a function F that is holomorphic in a neighbourhood of and such that the error F − f is uniformly bounded in the disk . |
2. | The corona theorem for when dim(E) < ∞: If there exists a δ > 0 such that for all , , then there exists a such that for all , g(z)f(z) = I. |
3. | The problem of complementing to an isomorphism for when {dim(E) < ∞ (Tolokonnikov’s lemma): has a left inverse iff it is a ‘part’ of an invertible element F in . |
4.
We consider Dirichlet spaces (
) in L
2 and more general energy forms
in L
p
,
. For the latter we introduce the notions of an extended ’Dirichlet’ space and a transient form. Under the assumption that
, resp.
, are compactly embedded in L
2, resp. L
p
, we prove a Poincaré inequality for transient (Dirichlet) forms. If both
and its adjoint
are sub-Markovian semigroups, we show that the transience of T
t
is independent of
) and that it is implied by the transience of the energy form
of
and the form
belonging to
. 相似文献
5.
Alejandra Maestripieri Francisco Martínez Pería 《Integral Equations and Operator Theory》2007,59(2):207-221
The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded)
J-selfadjoint operator A (with the unique factorization property) acting on a Krein space
and a suitable closed subspace
of
, the Schur complement
of A to
is defined. The basic properties of
are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive
operators on a Hilbert space.
To the memory of Professor Mischa Cotlar 相似文献
6.
Nathan S. Feldman 《Integral Equations and Operator Theory》2007,58(2):153-173
A pair of commuting operators, (A,B), on a Hilbert space
is said to be hypercyclic if there exists a vector
such that {A
n
B
k
x : n, k ≥ 0} is dense in
. If f, g ∈H
∞(G) where G is an open set with finitely many components in the complex plane, then we show that the pair (M
*
f
, M
*
g
) of adjoints of multiplcation operators on a Hilbert space of analytic functions on G is hypercyclic if and only if the semigroup they generate contains a hypercyclic operator. However, if G has infinitely many components, then we show that there exists f, g ∈H
∞(G) such that the pair (M
*
f
, M
*
g
) is hypercyclic but the semigroup they generate does not contain a hypercyclic operator. We also consider hypercyclic n-tuples. 相似文献
7.
On The Extended Eigenvalues of Some Volterra Operators 总被引:2,自引:0,他引:2
Srdjan Petrovic 《Integral Equations and Operator Theory》2007,57(4):593-598
We show that a large class of compact quasinilpotent operators has extended eigenvalues. As a consequence, if V is such an operator, then the associated spectral algebra
contains its commutant {V}' as a proper subalgebra. 相似文献
8.
Janez Bernik 《Archiv der Mathematik》2007,88(6):481-490
Let K be an algebraically closed field of arbitrary characteristic and F < K a subfield. If
is an irreducible semigroup of matrices such that the spectra of all the elements of
are contained in F, then
is conjugate to a subsemigroup of M
n
(F).
Research supported in part by the Ministry of Higher Education, Science, and Technology of Slovenia.
Received: 6 April 2006 相似文献
9.
We study the relative position of four (closed) subspaces in a Hilbert space. For any positive integer n, we give an example of exotic indecomposable system
of four subspaces in a Hilbert space whose defect is
. By an exotic system, we mean a system which is not isomorphic to any closed operator system under any permutation of subspaces.
We construct the examples using certain nice sequences construced by Jiang and Wang in their study of strongly irreducible
operators.
Dedicated to Professor Masahiro Nakamura on his 88th birthday 相似文献
10.
Victor Katsnelson 《Complex Analysis and Operator Theory》2009,3(1):147-220
The paper deals with root location problems for two classes of univariate polynomials both of geometric origin. The first
class discussed, the class of Steiner polynomial, consists of polynomials, each associated with a compact convex set . A polynomial of this class describes the volume of the set V + tB
n
as a function of t, where t is a positive number and B
n
denotes the unit ball in . The second class, the class of Weyl polynomials, consists of polynomials, each associated with a Riemannian manifold , where is isometrically embedded with positive codimension in . A Weyl polynomial describes the volume of a tubular neighborhood of its associated as a function of the tube’s radius. These polynomials are calculated explicitly in a number of natural examples such as balls,
cubes, squeezed cylinders. Furthermore, we examine how the above mentioned polynomials are related to one another and how
they depend on the standard embedding of into for m > n. We find that in some cases the real part of any Steiner polynomial root will be negative. In certain other cases, a Steiner
polynomial will have only real negative roots. In all of this cases, it can be shown that all of a Weyl polynomial’s roots
are simple and, furthermore, that they lie on the imaginary axis. At the same time, in certain cases the above pattern does
not hold.
Erasmus Darwin, the nephew of the great scientist Charles Darwin, believed that sometimes one should perform the most unusual experiments. They usually yield no results but when they do . . . . So once he played trumpet in front of tulips for the whole day. The experiment yielded no results.Submitted: March 5, 2007., Revised: February 1, 2008., Accepted: February 2, 2008. 相似文献
11.
The purpose of this paper is to give new and general characterizations for uniform dichotomy and uniform exponential dichotomy
of evolution families on the real line. We consider two general classes denoted
and
and we prove that if V,W are Banach function spaces with
and
, then the admissibility of the pair
for an evolution family
implies the uniform dichotomy of
. In addition, we consider a subclass
and we prove that if
, then the admissibility of the pair
implies the uniform exponential dichotomy of the family
. This condition becomes necessary if
. Finally, we present some applications of the main results. 相似文献
12.
We consider hypercyclic composition operators on
which can be obtained from the translation operator using polynomial automorphisms of
. In particular we show that if C
S
is a hypercyclic operator for an affine automorphism S on
, then
for some polynomial automorphism Θ and vectors a and b, where I is the identity operator. Finally, we prove the hypercyclicity of “symmetric translations” on a space of symmetric analytic
functions on ℓ1.
Received: 8 June 2006 Revised: 26 September 2006 相似文献
13.
Heinz Langer Alexander Markus Vladimir Matsaev 《Integral Equations and Operator Theory》2009,63(4):533-545
In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub–Matsaev condition on some interval Δ0 and is boundedly invertible in the endpoints of Δ0, then the ‘embedding’ of the original Hilbert space into the Hilbert space , where the linearization of A(z) acts, is in fact an isomorphism between a subspace of and . As a consequence, properties of the local spectral function of A(z) on Δ0 and a so-called inner linearization of the operator function A(z) in the subspace are established.
相似文献
14.
Ilwoo Cho 《Complex Analysis and Operator Theory》2007,1(3):367-398
We identify two noncommutative structures naturally associated with countable directed graphs. They are formulated in the
language of operators on Hilbert spaces. If G is a countable directed graphs with its vertex set V(G) and its edge set E(G), then we associate partial isometries to the edges in E(G) and projections to the vertices in V(G). We construct a corresponding von Neumann algebra
as a groupoid crossed product algebra
of an arbitrary fixed von Neumann algebra M and the graph groupoid
induced by G, via a graph-representation (or a groupoid action) α. Graph groupoids are well-determined (categorial) groupoids. The graph
groupoid
of G has its binary operation, called admissibility. This
has concrete local parts
, for all e ∈ E(G). We characterize
of
, induced by the local parts
of
, for all e ∈ E(G). We then characterize all amalgamated free blocks
of
. They are chracterized by well-known von Neumann algebras: the classical group crossed product algebras
, and certain subalgebras
(M) of operator-valued matricial algebra
. This shows that graph von Neumann algebras identify the key properties of graph groupoids.
Received: December 20, 2006. Revised: March 07, 2007. Accepted: March 13, 2007. 相似文献
15.
In 1993, Y. A. Abramovich, C. D. Aliprantis and O. Burkinshaw showed that every continuous operator with modulus on an lp-space (1 ≤ p < ∞) whose modulus commutes with a non-zero positive operator T on lp that is quasinilpotent at a non-zero positive vector x0 has a non-trivial invariant closed subspace. In this paper, it is proved that if
is a collection of continuous operators with moduli on lp that is finitely modulus-quasinilpotent at a non-zero positive vector x
0 then
and its right modulus sub-commutant
have a common non-trivial invariant closed subspace. In particular, all continuous operators with moduli on l
p
whose moduli commute with a non-zero positive operator I on l
p
that is quasinilpotent at a non-zero positive vector x
0 have a common non-trivial invariant closed subspace, so that all positive operators on l
p
which commute with a non-zero positive operator S on l
p
that is quasinilpotent at a non-zero positive vector x
0 have a common non-trivial invariant closed subspace.
This research was supported by the Natural Science Foundation of Hunan Province of P. R. China (04JJ6004), the Foundation
of Education Department of Hunan Province of P. R. China (04C002) and the Natural Science Foundation of P. R. China (10671147).
Received: 4 December 2005 Revised: 19 June 2006 相似文献
16.
Henrik Petersson 《Integral Equations and Operator Theory》2007,57(3):413-423
We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies
, the conjugate operator
is hypercyclic on the space S(H) of self-adjoint operators on H provided with the topology of uniform convergence on compact sets. That is, there exists an
such that
is dense in S(H). We generalize the result to more general conjugate maps
, and establish similar results for other operator classes in the algebra B(H) of bounded operators, such as the ideals K(H) and N(H) of compact and nuclear operators respectively. 相似文献
17.
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献
18.
Onur Yavuz 《Integral Equations and Operator Theory》2007,58(3):433-446
We consider a multiply connected domain
where
denotes the unit disk and
denotes the closed disk centered at
with radius r
j
for j = 1, . . . , n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains ∂Ω and does not contain the points λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded, then there exists a nontrivial common invariant subspace for T
* and (T − λ
j
I)*-1. 相似文献
19.
Let Q(x, y) = 0 be an hyperbola in the plane. Given real numbers β ≡ β (2n)={ β ij } i,j ≥ 0,i+j ≤ 2n , with β00 > 0, the truncated Q-hyperbolic moment problem for β entails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x, y) = 0, such that
We prove that β admits a Q-representing measure μ (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated, has a column relation Q(X,Y) = 0, and the algebraic variety
associated to β satisfies card
In this case,
if
then β admits a rank
-atomic (minimal) Q-representing measure; if
then β admits a Q-representing measure μ satisfying
相似文献
20.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献